Active Control of Dynamic Stall over a NACA 0012 Using NS-DBD Plasma Actuator

ACTIVE CONTROL OF DYNAMIC STALL OVER A NACA 0012

USING NS-DBD PLASMA ACTUATORS

A THESIS

Presented in Partial Fulfillment of the Requirements

for Graduation with Honors Research Distinction in

Aeronautical and Astronautical Engineering at

The Ohio State University

By

Nicole L. Whiting

*******

The Ohio State University

April 2018

ii

ABSTRACT

Dynamic stall occurs in applications where airfoils are rapidly changing angle of attack,

like rotorcraft or wind turbines. When the change is fast enough, flow over a pitching airfoil

remains attached beyond the static stall angle. This results in the formation of a dynamic stall

vortex (DSV) on the leading edge of the airfoil, which eventually convects over the airfoil and

sheds. During DSV convection and the accompanied flow separation, unsteady aerodynamic

loads are produced. These loads can lead to fatigue and eventually structural failure, making it

essential to mitigate the effects of dynamic stall. Nanosecond Dielectric Barrier Discharge

(NS-DBD) plasma actuators have shown promise at mitigating dynamic stall and reattaching the flow

over a NACA 0015 airfoil, a thick, symmetric airfoil, significantly reducing unsteady loads. A

high-voltage nanosecond pulse drives the actuator and creates rapid, localized heating that results in

a thermal perturbation. The thermal perturbation then excites the flow’s natural instabilities and

generates coherent flow structures. Previous work has shown that high Strouhal number

(non-dimensional frequency) excitation results in small structures that quickly develop, breakdown,

and result in smooth, partial reattachment of the flow whereas low Strouhal number excitation

results in large structures that are capable of fully reattaching the flow cyclically and lead to

unsteady loads. This work aims at improving upon the previous work by upgrading the facility

and data acquisition and reduction systems and using a thin airfoil to make the results more

relevant to rotorcraft applications. A NACA 0012 airfoil is chosen because it is a well-documented,

thin airfoil. Facility upgrades include integrating all systems into a National Instruments

CompactRIO, which will allow for better synchronization between all control systems and

iii

servo, this allows for more accurate pitching angles over the previous setup, which used belts

that could stretch and cause a phase delay. Previously the lift and drag on the airfoil were

calculated by integrating pressure measurements which introduced error due to potential

three-dimensionality in the flow. Therefore, a load cell will be used instead to directly measure the

forces and momentum on the airfoil. Mitigating the negative effects of dynamic stall has the

potential to increase the lifespan of blades and increase lift, which will allow rotorcraft to fly

iv

ACKNOWLEDGEMENTS

I would like to thank Professor Mo Samimy for giving me the opportunity to work with his

group and for all of the help he has given me along the way. I would also like to thank Dr. Nathan

Webb who has taught me a great deal this year. His knowledge, patience, and willingness to

always help, no matter how busy he was, is truly amazing. Finally, I would like to thank David

v TABLE OF CONTENTS ABSTRACT ... ii ACKNOWLEDGEMENTS ... iv TABLE OF CONTENTS ... v LIST OF FIGURES ... vi CHAPTER 1: Introduction ... 1 CHAPTER 2: Background ... 4 2.1 Introduction ... 4 2.2 Dynamic Stall ... 4 2.3 Flow Control ... 5 2.4 NS-DBD ... 7

CHAPTER 3: Previous Research ... 8

3.1 Introduction ... 8

3.2 Results ... 8

CHAPTER 4: Shortcomings of Previous System and Their Mitigation ... 13

4.1 Introduction ... 13

4.2 Airfoil ... 13

4.3 Force and Moment Measurements ... 15

4.4 Servo-Optical Access ... 17

4.5 Control System ... 20

CHAPTER 5: Conclusions and Future Work ... 22

vi

LIST OF FIGURES

Figure 2.1. Illustration of dynamic stall [7]. ... 5

Figure 2.2. NS-DBD plasma actuator schematic [4]. Thickness is exaggerated for clarity. ... 7

Figure 3.1. Phase-averaged swirling strength at Re=300,000, k=0.050 and Ste=0.35. Pitching down from 20 to 17 degrees [4]. ... 9

Figure 3.2. Phase-averaged swirling strength at Re=300,000, k=0.050 and Ste=9.9. Pitching down from 20 to 17 degrees [4]. ... 10

Figure 3.3. Phase-averaged lift and moment coefficient at Re=300,000 and k=0.050. Darker colors represent pitch up and lighter colors represent pitch down. [4] ... 10

Figure 3.4. Reattachment angle of attack versus the excitation Strouhal number at Re=300,000 and k=0.050 [4]. ... 11

Figure 3.5. Normalized reduction in baseline moment coefficient peak versus excitation Strouhal number at Re=176,000 and k=0.05 [4]. ... 12

Figure 4.1. Static coefficient of lift vs angle of attack [6]. ... 14

Figure 4.2. NACA 0012 airfoil with a replaceable Delrin leading edge. ... 15

Figure 4.3. Static pressure tap distribution [6]. ... 16

Figure 4.4. Airfoil mounted on the load cell. ... 17

Figure 4.5. Airfoil motion vs time [6]. ... 18

Figure 4.6. Photographs of oscillating mechanism [6]. ... 19

Figure 4.7. Airfoil, load cell and servo motor setup. ... 19

1

CHAPTER 1: Introduction

Rotorcraft are extremely important because of their ability to take off and land without a

runway and hover in place. Because of these abilities, they are often used in specialized tasks like

national defense, fire and rescue and medical transport. While these enhance capabilities make

rotorcraft important, they also complicate the aerodynamics. In order to maintain lift symmetry

in the rotor, the retreating blades need to be at a significantly higher angle of attack than the

advancing blades [1]. Therefore, the blades need to be constantly changing angle of attack as

they rotate around the rotor. After pitching a retreating blade to a higher angle of attack than

the static stall angle, during pitch up or eventual pitch down, the flow can no longer remain

attached to the blades and a phenomenon called dynamic stall can occur.

Dynamic stall occurs in applications where airfoils are rapidly changing angle of attack,

when the change is fast enough, flow over a pitching airfoil remains attached beyond the static

stall angle. This results in the formation of a dynamic stall vortex (DSV) on the leading edge of the

airfoil, which eventually convects over the airfoil and sheds. During DSV convection and the

accompanied flow separation, unsteady aerodynamic loads are produced. These unsteady loads

produce a rapid growth in blade torsion which can lead to fatigue and eventually structural

failure. Due to these issues, dynamic stall is normally the limiting factor in the operational flight

envelope of helicopters [1]. Therefore, in order to increase operating conditions of rotorcraft it

is essential to mitigate the effects of dynamic stall.

Conventionally, research in this field uses passive and occasionally active flow control

devices to mitigate dynamic stall by eliminating the dynamic stall vortex. A common passive

2

because changing the airfoil shape can increase the weight of the blade and change its

aerodynamic properties making it ineffective at off-design operating conditions. Active

techniques include the use of momentum injectors and plasma actuators. Momentum injectors

typically add momentum to the flow via blowing jets [3]. As the speed is increased, more

momentum is needed to sustain control efficacy. This increases the complexity and cost of the

airfoils, but they have the potential to maintain a broad operating range if the required

momentum could be maintained. Plasma actuators, on the hand, are minimally complex and can

still maintain a broad operating range making them ideal for rotorcraft.

Previous research done in the Gas Dynamics and Turbulence Laboratory at Ohio State [4],

has shown promise at mitigating dynamic stall and reattaching the flow over a NACA 0015 airfoil

using a Nanosecond Dielectric Barrier Discharge (NS-DBD) plasma actuator. A high-voltage

nanosecond pulse drives the actuator and creates rapid, localized heating that results in a

thermal perturbation. The thermal perturbation then excites the flow’s natural instabilities and

generates coherent flow structures, which entrain high-momentum free stream air near the

low-momentum airfoil surface, energizing the flow and reducing the chance for separation [5]. The

plasma actuators consist of two copper electrodes separated by a dielectric barrier; they require

a relatively low power input, which allows them to remain effective at high speeds. They are also

less than 0.5mm thick, meaning the aerodynamic properties of the blades are relatively

unchanged [6].

This work aims at improving upon the previous work in the Gas Dynamics and Turbulence

Laboratory at Ohio State [4, 6] by making facility and instrumentation upgrades. This thesis

3

from the previous experimental setup in Chapter 3. Details the shortcomings in the previous

experimental setup and data acquisition and reduction, and steps taken in the current work to

mitigate them in Chapter 4. Finally, concluding remarks and future work are discussed in Chapter

4

CHAPTER 2: Background 2.1 Introduction

Rotorcraft experience dynamic stall because the retreating rotor blades are rapidly

changing angle of attack, therefore the flow over a pitching blade remains attached beyond the

static stall angle. This leads to the formation and shedding of the dynamic stall vortex and

unsteady loads over the blade and ultimately limits the operational flight envelope of the

rotorcraft. To increase the operational capabilities of rotorcraft, the effects of dynamic stall need

to be mitigated. NS-DBD plasma actuators have shown promise at mitigating dynamic stall and

reattaching the flow over a NACA 0015 airfoil, significantly reducing unsteady loads.

2.2 Dynamic Stall

Dynamic stall is characterized in five states, shown below in Figure 2.1 [7]. The first state

occurs when the maximum angle of attack of the airfoil is less than the static stall angle. The

second state occurs when the maximum angle of attack equals the static stall angle, at this point

a leading-edge vortex starts forming. During both of these states, the aerodynamic loads behave

similarly to the static case and the flow is attached. The maximum angle of attack can continue

to increase past the static stall angle because the airfoil pitching motion leads to the formation

of dynamic stall vortex near the leading edge of the airfoil [1]. As the maximum angle of attack

continues to increase past the static stall angle the lift generated by the airfoil also continues to

increases and the leading-edge vortex convects over the airfoil due to the accumulation of

vorticity near the leading edge and sheds, this is the third state. Once the vortex passes the

trailing edge, the airfoil is fully stalled, this is the fourth state. Finally, the fifth state occurs when

5

Figure 2.1. Illustration of dynamic stall [7].

2.3 Flow Control

Conventionally, research in this field uses passive and occasionally active flow

control devices to mitigate dynamic stall by eliminating the dynamic stall vortex. A common

passive technique includes making geometric modifications to the airfoil [2]. This can be

problematic because changing the airfoil shape can increase the weight of the blade and change

6

techniques include the use of momentum injectors and plasma actuators. Momentum injectors

can add momentum to the flow by a variety of techniques including fluidic, piezoelectric,

electromagnetic, and electrostatic [8]. As the flow speed is increased, more momentum is

needed to sustain control efficacy, therefore these techniques become more expensive and less

practical. Overall, momentum injectors increase the complexity and cost of the airfoils, but they

have the potential to maintain a broad operating range if the required momentum could be

maintained. Plasma actuators, on the other hand, are minimally complex, require relatively low

power and can still maintain a broad operating range making them ideal for rotorcraft. The

installation of dielectric barrier discharge (DBD) plasma actuators are relatively simple, as they

are simply placed on the leading edge of airfoil, they minimally effect the flow field when not in

use and they can potentially be retrofitted to existing airfoils. The earliest form of DBD plasma

actuators were alternating current driven (AC-DBD) plasma actuators. AC-DBD plasma actuators

are momentum based, therefore as the speed of the aircraft increases the momentum needed

also increases, but the ion density in the region of the electric charge restricts the momentum

production [8]. Therefore, AC-DBD plasma actuators are currently limited at higher speeds. As a

result, a new driving waveform has been applied to the DBD actuators, nanosecond high voltage

DC pulses, and they are called nanosecond DBD (NS-DBD) plasma actuators. Even though the

physical construction of AC-DBD and NS-DBD are similar, their control mechanisms are very

different because of how they are driven. NS-DBD actuators are thermal based and therefore

7

2.4 NS-DBD

NS-DBD plasma actuators are minimally complex, they consist of two 0.09 mm thick

copper tape electrodes separated by a dielectric layer composed of three layers of 0.09 mm thick

Kapton tape, making the total thickness of the actuator 0.45 mm, shown in Figure 2.2 below.

They are powered by a custom, in-house manufactured pulse generator that sends high-voltage

nanosecond pulses to the copper electrodes, producing the perturbations. The pulse generator

is powered by a 450 VDC power supply [4]. The actuator is placed just downstream of the leading

edge where the shear layer over the airfoil is formed and its natural instability is most receptive

to the perturbations. This reduces the energy consumption of the actuators which on average is,

12.6 mJ per pulse. Overall, the high-voltage nanosecond pulse drives the actuator and creates

rapid, localized heating that results in a thermal perturbation. The thermal perturbation then

excites the flow’s natural instabilities and generates coherent flow structures, which entrain

high-momentum free stream air near the low-momentum airfoil surface, energizing the flow and

reducing the chance for separation [5].

8

CHAPTER 3: Previous Research 3.1 Introduction

A NACA 0015 airfoil was mounted in the recirculating wind tunnel located at the

Aerospace Research Center. The airfoil was connected to an oscillating mechanism that varied

the angle of attack sinusoidally. A plasma actuator was mounted just downstream of the airfoil

leading edge at x/L=0.01. Baseline experiments were done with the plasma actuator installed but

not excited, to understand it’s effect on the flow physics. Experiments were done for three

Reynolds numbers (dimensionless ratio of inertial forces to viscous forces) based on the airfoil

cord (Re=167,000, 300,000 and 500,000), at three reduced frequencies (k=0.025, 0.050, and

0.075) and 20 excitation Strouhal numbers ranging from 0 – 9.9. Detailed unsteady surface

pressure measurements, and flow velocity and turbulence measurements were taken to assess

the effect of control.

3.2 Results

The work resulted in three major conclusions [4]: high Strouhal number excitation results

in small structures and low Strouhal number excitation results in large structures, all excited cases

resulted in earlier flow reattachment, and excited cases had a decreased dynamic stall vortex

strength.

The first finding can be seen in Figures 3.1 and 3.2 below. They show the phase-averaged

swirling strength at a Reynolds number of 300,000 and a reduced frequency of 0.050 while the

airfoil is pitching down from 20 to 17 degrees. Figure 3.1 has an excitation Strouhal number of

0.35, whereas, Figure 3.2 has an excitation Strouhal number of 9.9. In Figure 3.1, a large structure

9

several significantly smaller structures formed over the airfoil and disintegrate while convecting

over the airfoil. While not shown, the large structure convects over the entire airfoil and sheds

from the airfoil leading to oscillatory forces and moments on the blade. As the Strouhal number

increased the oscillatory behavior smooths out. These effects are clearly shown in Figure 3.3 for

the lift and moment coefficients.

10

Figure 3.2. Phase-averaged swirling strength at Re=300,000, k=0.050 and Ste=9.9. Pitching down from 20 to 17 degrees [4].

Figure 3.3. Phase-averaged lift and moment coefficient at Re=300,000 and k=0.050. Darker colors represent pitch up and lighter colors represent pitch down. [4]

11

The next conclusion, all excited cases resulted in earlier flow reattachment, is shown

below in Figure 3.4. The baseline reattachment angle of attack was 7.2 degrees. Exciting the flow

with a Strouhal number of 0.35 produced the largest differential increase in the reattachment

angle jumping from 7.2 to 8.5 degrees. As the Strouhal number continued to increase, it produced

a general upward trend of reattaching the flow earlier; overall, every excited case reattached the

flow earlier than the baseline test.

Figure 3.4. Reattachment angle of attack versus the excitation Strouhal number at Re=300,000 and k=0.050 [4].

The final conclusion, excited cases had a decreased dynamic stall vortex, is shown below

in Figure 3.5. Due to the poor temporal resolution in the PIV data, the strength of the dynamic

stall vortex could not be directly determined, but a normalized reduction in moment coefficient

12

Strouhal number increases the normalized reduction in baseline moment coefficient peak

increases. This means the magnitude of the peak moment coefficient is decreasing. Once it

plateaus, it means the dynamic stall vortex is suppressed. At a Reynolds number of 176,000 and

a reduced frequency, the dynamic stall vortex is suppressed at an excitation Strouhal number of

eight.

Figure 3.5. Normalized reduction in baseline moment coefficient peak versus excitation Strouhal number at Re=176,000 and k=0.05 [4].

Overall, this research shows high Strouhal number excitation results in small

structures that quickly develop, breakdown, and result in smooth, partial reattachment of the

flow, whereas low Strouhal number excitation results in large structures that are capable of fully

13

CHAPTER 4: Shortcomings of Previous System and Their Mitigation 4.1 Introduction

Based on the previous research, NS-DBD plasma actuators show promise at suppressing

dynamic stall and reattaching the flow over a NACA 0015 airfoil, significantly reducing unsteady

loads. Due to design of the facility and the instrumentation used, there are some shortcomings

in the repeatability, generating significant uncertainties in the collected data. The results are also

not directly relatable to rotorcraft due to the type of airfoil used. The following sections will go

over each of the shortcomings and the solution to address them.

4.2 Airfoil

A NACA 0015 airfoil is characterized as a thick airfoil because its maximum thickness to

chord ratio is 15 percent. Thick airfoils experience trailing edge stall. Rotorcraft, on the other

hand, typically use thin airfoils and thin airfoils experience leading edge stall. Therefore, the

previous results cannot be directly related to rotorcraft because the airfoil tested experiences a

different type of flow separation. As a result, a NACA 0012 airfoil was manufactured for future

experiments. It is a thin, symmetric airfoil with a maximum thickness to chord ratio of 12 percent.

This specific airfoil was chosen because it is well characterized in literature.

Another concern with the previous airfoil was its size creating too much blockage in the

wind tunnel and potentially skewing the results. The static coefficient of lift versus angle of attack

for the previous setup and results from literature are shown below in Figure 4.1. They both show

that the static stall angle is 13 degrees, but the airfoil used in the previous study has a much

sharper stall. The NACA 0015 airfoil has a chord of 8 in. therefore the new NACA 0012 airfoil was

14

to install the plasma actuators on, shown in Figure 4.2 below. This was done to prevent arcing

between the high voltage plasma actuators and the metal airfoil. The material Delrin was chosen

because it a synthetic polymer with a high stiffness. In the event that the leading edge does get

damaged, it can easily be replaced.

15

Figure 4.2. NACA 0012 airfoil with a replaceable Delrin leading edge.

4.3 Force and Moment Measurements

In the previous setup, 35 static pressure taps were located on the surface of the airfoil in

order to calculate the phase-averaged pressure coefficient, Figure 4.3. From these pressure

measurements the lift, drag and moment were calculated. Due to the long pressure tap lines

from the airfoil to the data acquisition system, empirical lag/gain corrections were applied to the

data. Overall, this system of calculating the lift, drag and moment introduced error due to the

potential three-dimensionality in the flow. Therefore, the new system directly measures the lift,

drag and moment using an ATI SI-660-60 6-axis force/torque transducer with great resolution,

16

Figure 4.3. Static pressure tap distribution [6]. Table 1. Load cell sensing range and resolution.

Sensing Range Resolution

Fx 660 N 1/8 N Fy 660 N 1/8 N Fz 1980 N 1/4 N Tx 60 Nm 10/1333 Nm Ty 60 Nm 10/1333 Nm Tz 60 Nm 10/1333 Nm

17

Figure 4.4. Airfoil mounted on the load cell.

4.4 Servo-Optical Access

For dynamic stall experiments, the airfoil needs to be consistently changing angle of

attack to simulate flight conditions; to do this the previous setup used a servomotor driven by

timing belts. There are two main concerns with the previous setup, first the timing belts can

stretch over time creating a phase delay and second the overall setup reduced the optical access.

The cycle-to-cycle motion of the servo is shown below in Figure 4.5, it was oscillated

sinusoidally from 8 to 18 degrees at a frequency of 3.48 Hz. The individual cycles varied up to a

18

repeatability standpoint, if the actual motion of the airfoil is unknown, the actual stall

characteristics are also unknown. This can be attributed to the timing belts, over time they tend

to stretch or slip. To counteract this, the new setup uses a direct drive servo that is accurate to a

thousandth of a degree.

Figure 4.5. Airfoil motion vs time [6].

To secure the airfoil in the wind tunnel, its ends were connected to disks in the sidewall

of the wind tunnel. The disks were then driven by the servomotor-timing belt combination,

shown below in Figure 4.6. The disks in the sidewall of the wind tunnel obstructs the view near

the trailing edge of the airfoil in Particle Image Velocimetry (PIV) measurements, therefore the

vortex shedding over the trailing edge is obstructed, an example of this is shown in Figures 3.1

and 3.2. PIV is a major optical measurement tool in obtaining detailed flow velocity and

turbulence measurements. If the setup obstructs optical access to the model, it makes the tool

significantly less useful in exploring flow physics. For that reason, the direct drive servomotor is

19

vertically on top of them, therefore there will be no obstructions in the optical access, shown in

Figures 4.7 and 4.8.

Figure 4.6. Photographs of oscillating mechanism [6].

20

Figure 4.8. Full setup mounted in the wind tunnel.

4.5 Control System

To control the system and collect data three data systems were used, these include a

National Instrument Data Acquisition (NI-DAQ) system, three Scanivalve Pressure Scanners (SPS),

and an ABB Servo Controller. To synchronize the NI-DAQ and the SPS a continuous chirp signal

was used. The chirp was transmitted to the NI-DAQ using LabVIEW and it was transmitted to the

SPS using a speaker. The constant lag between the inputs and outputs were determined and

21

achieved by aligning the analog output of the servo to the position given by the network

connection.

Having three data acquisition systems can introduce synchronization errors, which is

extremely detrimental to dynamic stall tests since dynamic stall is time dependent. Therefore,

the new system uses a NI-CompactRIO (CRIO). It has a real-time processor, a user-programmable

FPGA, and interchangeable modules for each instrument, this ensure complete synchronization

22

CHAPTER 5: Conclusions and Future Work

Dynamic stall occurs in applications where airfoils are rapidly changing angle of attack.

When the change is fast enough, flow over a pitching airfoil remains attached beyond the static

stall angle. This results in the formation of a dynamic stall vortex (DSV) on the leading edge of the

airfoil, which eventually convects over the airfoil and sheds. During DSV convection and the

accompanied flow separation, unsteady aerodynamic loads are produced. These unsteady loads

produce a rapid growth in blade torsion which can lead to fatigue and eventually structural

failure. Due to these issues, dynamic stall is normally the limiting factor in the operational flight

envelope of helicopters. Therefore, in order to increase operating conditions of rotorcraft it is

essential to mitigate the effects of dynamic stall. Previous research has shown promise at

mitigating dynamic stall and reattaching the flow over a NACA 0015 airfoil using a NS-DBD plasma

actuator. This work aims at improving upon the previous work by changing the airfoil to a NACA

0012 to make it more relevant to rotorcraft, using a load cell to directly measure the forces and

moments on the airfoil, changing to a direct-drive servo to mitigate the cycle-to-cycle motion

variation, and incorporating all systems into one control system to ensure complete

synchronization.

Future work includes detailed unsteady lift, drag, and moment and flow velocity and

turbulence measurements, at the same parameters tested with the old setup but with the new

experimental setup. This is to verify that the same trends are seen and that they can be applied

to rotorcraft, by using the thin airfoil. Additional excitation Strouhal numbers will be tested to

determine if there is an optimum value. Due to the upgraded system, higher excitation Strouhal

23

to see the dynamic stall vortex and the subsequent excitation structures; this will greatly improve

the understanding of the flow physics. Overall, this research is being conducted to mitigate the

negative effects of dynamic stall, which has the potential to increase the lifespan of the blades

24

CHAPTER 6: References

[1] J. G. Leishman, Principles of Helicopter Aerodynamics, 2 ed., Cambridge: Cambridge University Press, 2006.

[2] W. Joo, B. Lee, K. Yee, and D. Lee, "Combining Passive Control Method for Dynamic Stall Control," Journal of Aircraft, Vol. 43, No. 4, pp. 1120-1128, 2006.

[3] D. Weaver, K. W. McAlister and J. Tso, "Suppression of Dynamic Stall by Steady and Pulsed Upper-Surface Blowing," NASA, Moffett Field, 1996.

[4] A. Singhal, D. Castaneda, N. Webb, and M. Samimy, “Control of Dynamic Stall over a NACA 0015 Airfoil using NS-DBD Plasma Actuators,” AIAA Journal, Vol. 56, No. 1, pp. 78-89, 2018. [5] J. Little, K. Takashima, M. Nishihara, I. Adamovich, and M. Samimy, “Separation Control with Nanosecond Pulse Driven Dielectric Barrier Discharge Plasma Actuators,” AIAA Journal, Vol. 50, pp. 350-365, 2012.

[6] A. Singhal, "Unsteady Flow Separation Control over a NACA 0015 using NS-DBD Plasma Actuators," M.S. Thesis, Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, 2016.

[7] T. C. Corke and F. O. Thomas, "Dynamic Stall in Pitching Airfoils: Aerodynamic Damping and Compressibility Effects," Annual Review of Fluid Mechanics, pp. 479- 505, 2015.

[8] C. Rethmel, J. Little, K. Takashima, M. Nishihara, I. Adamovich, and M. Samimy, “Flow

Separation Control over and Airfoil with Nanosecond Pulse Driven DBD Plasma Actuators,” International Journal of Flow Control, Vol. 3, No. 4, pp. 213-232, 2011.